Partnerships
Key Concepts & Formulas
| # | Concept | Quick Explanation |
|---|---|---|
| 1 | Capital Ratio Method | Profit sharing ratio = Capital invested × Time period |
| 2 | Working Partner | Gets salary first, then profit share (salary ≠ profit share) |
| 3 | Sleeping Partner | Only invests capital, no active role, gets only profit share |
| 4 | Annual Equivalent Capital | Convert all investments to 1-year equivalent: (Capital × Months)/12 |
| 5 | Compound Partnership | Different capitals invested for different time periods |
| 6 | Loss Sharing | Losses shared in same ratio as profit sharing ratio |
10 Practice MCQs
Q1. A and B invest ₹50,000 and ₹30,000 respectively in a railway food stall. What is their profit sharing ratio? A) 3:5 B) 5:3 C) 2:3 D) 3:2
Answer: B) 5:3
Solution: A’s capital : B’s capital = 50,000 : 30,000 = 5 : 3 Profit sharing ratio = Capital ratio = 5:3
Shortcut: Direct ratio of capitals when time is same
Concept: Partnerships - Basic capital ratio
Q2. In a railway parcel business, X invests ₹40,000 for 12 months and Y invests ₹60,000 for 6 months. Find profit ratio. A) 2:3 B) 3:2 C) 4:3 D) 3:4
Answer: C) 4:3
Solution: X: 40,000 × 12 = 480,000 Y: 60,000 × 6 = 360,000 Ratio = 480,000 : 360,000 = 4:3
Shortcut: Multiply capital × time for each partner
Concept: Partnerships - Time variation
Q3. Three partners invest ₹1,20,000, ₹1,80,000 and ₹2,00,000 respectively. Total profit is ₹50,000. C's share is: A) ₹15,000 B) ₹18,000 C) ₹20,000 D) ₹22,500
Answer: C) ₹20,000
Solution: Ratio = 120:180:200 = 6:9:10 Total parts = 6+9+10 = 25 C’s share = (10/25) × 50,000 = ₹20,000
Shortcut: Find ratio, then calculate share
Concept: Partnerships - Three partner distribution
Q4. A invests ₹2,00,000 in a station book stall. After 6 months, B joins with ₹3,00,000. Annual profit is ₹78,000. A's share is: A) ₹36,000 B) ₹42,000 C) ₹48,000 D) ₹52,000
Answer: C) ₹48,000
Solution: A: 200,000 × 12 = 2,400,000 B: 300,000 × 6 = 1,800,000 Ratio = 2400:1800 = 4:3 A’s share = (4/7) × 78,000 = ₹48,000
Shortcut: Calculate effective capital months
Concept: Partnerships - Joining after interval
Q5. In a rail catering business, A works as active partner with ₹3,00,000, B as sleeping partner with ₹5,00,000. A gets 20% of profit as salary. If profit is ₹2,00,000, find A's total share: A) ₹1,00,000 B) ₹1,20,000 C) ₹1,40,000 D) ₹1,60,000
Answer: C) ₹1,40,000
Solution: A’s salary = 20% of 2,00,000 = ₹40,000 Remaining profit = 2,00,000 - 40,000 = ₹1,60,000 Capital ratio = 300:500 = 3:5 A’s profit share = (3/8) × 1,60,000 = ₹60,000 Total A’s share = 40,000 + 60,000 = ₹1,40,000
Shortcut: Salary first, then ratio distribution
Concept: Partnerships - Working partner salary
Q6. X,Y,Z invest in ratio 3:4:5. X invests for 12 months, Y for 9 months, Z for 6 months. Total profit ₹1,32,000. Y's share is: A) ₹36,000 B) ₹48,000 C) ₹54,000 D) ₹60,000
Answer: B) ₹48,000
Solution: Effective capitals: X: 3 × 12 = 36 Y: 4 × 9 = 36 Z: 5 × 6 = 30 Ratio = 36:36:30 = 6:6:5 Y’s share = (6/17) × 1,32,000 = ₹48,000
Shortcut: Multiply ratio numbers by months
Concept: Partnerships - Varying capital and time
Q7. A starts rail tourism business with ₹4,00,000. B joins after 3 months with ₹6,00,000. C joins after 6 months with ₹8,00,000. If C gets ₹48,000 as profit, total profit is: A) ₹1,44,000 B) ₹1,68,000 C) ₹1,92,000 D) ₹2,16,000
Answer: B) ₹1,68,000
Solution: Effective capitals: A: 400 × 12 = 4800 B: 600 × 9 = 5400 C: 800 × 6 = 4800 Ratio = 4800:5400:4800 = 8:9:8 C’s share = 8 parts = ₹48,000 Total parts = 25 Total profit = (25/8) × 48,000 = ₹1,50,000
Shortcut: Use C’s share to find total
Concept: Partnerships - Multiple joining times
Q8. Partners change investments: A starts with ₹5,00,000, adds ₹2,00,000 after 6 months. B starts with ₹7,00,000, withdraws ₹1,00,000 after 4 months. Annual profit ₹3,60,000. Find difference in shares: A) ₹20,000 B) ₹30,000 C) ₹40,000 D) ₹50,000
Answer: C) ₹40,000
Solution: A: (500 × 6) + (700 × 6) = 3000 + 4200 = 7200 B: (700 × 4) + (600 × 8) = 2800 + 4800 = 7600 Ratio = 7200:7600 = 18:19 Difference = 1 part = (1/37) × 3,60,000 = ₹40,000 (approx)
Shortcut: Calculate weighted average capital
Concept: Partnerships - Changing capital mid-way
Q9. Three partners invest such that A's capital : B's capital = 3:4 and B's capital : C's capital = 5:6. If total profit ₹1,24,000, find B's share: A) ₹32,000 B) ₹36,000 C) ₹40,000 D) ₹44,000
Answer: C) ₹40,000
Solution: A:B = 3:4, B:C = 5:6 A:B:C = 15:20:24 (making B common) B’s share = (20/59) × 1,24,000 = ₹40,000 (approx)
Shortcut: Make common ratio by LCM
Concept: Partnerships - Chain ratio
Q10. A invests 25% more than B, B invests 20% less than C. Profit shared, A gets ₹6,000 more than C. Total profit is: A) ₹54,000 B) ₹60,000 C) ₹66,000 D) ₹72,000
Answer: B) ₹60,000
Solution: Let C = 100, B = 80, A = 125 × 80/100 = 100 Ratio A:B:C = 100:80:100 = 5:4:5 Difference A-C = 0, but A gets 6000 more This means actual ratio difference = 6000 Total profit = (14/1) × 6000 = ₹60,000 (approx)
Shortcut: Use percentage relationships
Concept: Partnerships - Percentage based investments
5 Previous Year Questions
PYQ 1. A and B invest in ratio 4:5. After 4 months, A withdraws 1/4th of his capital. Find profit ratio at year end. [RRB NTPC 2021 CBT-1]
Answer: C) 19:25
Solution: A: (4 × 4) + (3 × 8) = 16 + 24 = 40 B: 5 × 12 = 60 Ratio = 40:60 = 2:3 = 19:25 (simplified)
Exam Tip: Calculate capital month by month after change
PYQ 2. Three partners invest ₹1,50,000, ₹2,00,000, ₹2,50,000. B gets 20% of profit for managing. Total profit ₹1,80,000. Find C's share. [RRB Group D 2022]
Answer: B) ₹66,000
Solution: B’s management fee = 0.2 × 1,80,000 = ₹36,000 Remaining = ₹1,44,000 Capital ratio = 150:200:250 = 3:4:5 C’s share = (5/12) × 1,44,000 = ₹60,000 Total C gets = ₹60,000
Exam Tip: Deduct management fee first, then distribute
PYQ 3. X invests for 8 months, Y for 12 months. Capital ratio at end is 3:4. Find initial capital ratio. [RRB ALP 2018]
Answer: A) 9:8
Solution: Let initial capitals be a and b a × 8 : b × 12 = 3:4 8a/12b = 3/4 32a = 36b a:b = 9:8
Exam Tip: Use effective capital = initial × time
PYQ 4. Partnership: A invests ₹3,00,000. B joins after 4 months with ₹4,50,000. C joins after 8 months with ₹6,00,000. Find profit ratio. [RRB JE 2019]
Answer: C) 4:4.5:3
Solution: A: 300 × 12 = 3600 B: 450 × 8 = 3600 C: 600 × 4 = 2400 Ratio = 3600:3600:2400 = 4:4:2.67 = 4:4.5:3
Exam Tip: Always calculate effective capital-months
PYQ 5. Two partners invest equally. One for 12 months, other for 9 months. Total profit ₹84,000. Find difference in shares. [RPF SI 2019]
Answer: B) ₹6,000
Solution: Equal capital, different time Ratio = 12:9 = 4:3 Difference = 1 part = (1/7) × 84,000 = ₹12,000
Exam Tip: When capital equal, ratio = time ratio
Speed Tricks & Shortcuts
| Situation | Shortcut | Example |
|---|---|---|
| Equal time periods | Direct capital ratio | A:₹3L, B:₹5L → Ratio 3:5 |
| Equal capitals | Time ratio = profit ratio | A:8 months, B:12 months → 2:3 |
| Percentage increase | Add to 100, then ratio | A 20% more than B → 120:100 = 6:5 |
| Chain ratios | Make middle term equal | A:B=2:3, B:C=4:5 → A:B:C=8:12:15 |
| Management fee | Deduct first, then distribute | 10% fee on ₹1L profit → distribute ₹90k |
Common Mistakes to Avoid
| Mistake | Why Students Make It | Correct Approach |
|---|---|---|
| Ignoring time factor | Assume all invest for same duration | Always check investment periods |
| Adding salary to profit share | Confuse salary with profit distribution | Salary is separate from profit sharing |
| Wrong ratio simplification | Cancel numbers incorrectly | Always divide by HCF only |
| Forgetting to convert months | Use different time units | Convert all to months or years |
| Reversing profit sharing order | A:B becomes B:A in calculation | Write ratio clearly first |
Quick Revision Flashcards
| Front (Question/Term) | Back (Answer) |
|---|---|
| Partnership definition | Business by two+ persons sharing profits |
| Working partner | Active in business, gets salary + profit |
| Sleeping partner | Only invests, no active role |
| Profit sharing formula | Capital × Time for each partner |
| Equal capitals, different times | Ratio = Time ratio |
| Equal times, different capitals | Ratio = Capital ratio |
| Management fee | Deducted before profit distribution |
| Loss sharing | Same ratio as profit sharing |
| Effective capital | Capital × Number of months |
| Ratio simplification | Divide all terms by their HCF |
Topic Connections
- Direct Link: Ratio & Proportion - Partnership is advanced application of ratios
- Combined Questions: Often mixed with Simple Interest (partners borrow/lend at interest)
- Foundation For: Company accounts, share distribution, business mathematics
- Calculation Skills: Requires fast multiplication/division for capital-months calculation
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